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Chop said:
An S bin Lux III will be pretty close to a Q bin 1W at about 350mA. In any case, you'll be better off going with the Lux III. If you get a T bin, it should be brighter.
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There probably would be little if any noticable difference between an S Bin Luxeon III and a Q Bin Luxeon I at 350mA.
Driving a Luxeon III at half it's rated current produces light, but you will have a color shift such that a W0 tint will turn into an X0 or X1. The Luxeon I is binned at 350mA, and if you drive it at spec, it will preserve its tint at that lower current - the Luxeon III will not.
If you got with a Luxeon III, use the MM+. If you use the MM+ on a Luxeon I you will be overdriving the LED. MM Lite on a Luxeon I will give you more runtime and less heat due to lower drive currents, but less brightness as well.
Good luck.